SPRING UNIT 14. second half. Line symmetry and reflection. Measuring angles. Naming and estimating angles. Drawing angles
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1 PART SPRING second half SHAPE AND SPACE SECTION Line symmetry and reflection SECTION Measuring angles SECTION Naming and estimating angles SECTION Drawing angles SECTION 5 Calculations involving angles CROWN COPYRIGHT 00
2 NOTES FOR THE TEACHER SHAPE AND SPACE SUGGESTED TIME 5 hours TEACHING OBJECTIVES Recognise reflective symmetry and reflect shapes in a mirror line. Measure and draw lines to the nearest millimetre. Recognise directions, and perpendicular and parallel lines. Understand and use degrees. Use a protractor to measure and draw acute and obtuse angles to nearest. Calculate angles on a straight line. Identify, estimate and order acute and obtuse angles. Make patterns from rotating shapes. Recognise and explain patterns and relationships, generalise and predict. SECTION Line symmetry and reflection SECTION Measuring angles SECTION Naming and estimating angles SECTION Drawing angles SECTION 5 Calculations involving angles HOMEWORK Section, Star Challenges and on symmetry. Section, Star Challenge 5 is designed to reinforce mathematical language. Consolidate the use of a protractor to measure and draw angles. CROWN COPYRIGHT 00 8
3 PART CHECKLIST Unit Checklist for pupils Line symmetry and reflection You will: recognise reflective symmetry reflect shapes in a mirror line Measuring angles You will: use a protractor to measure angles to the nearest degree Naming and estimating angles You will: classify angles according to type and size estimate the size of angles Drawing angles You will: draw angles to the nearest degree draw and measure lines to the nearest millimetre Calculations involving angles You will: use the fact that angles on a straight line add up to 80 work out the size of unknown angles without using a protractor CROWN COPYRIGHT 00 9
4 SECTION : LINE SYMMETRY AND REFLECTION DIRECT TEACHING POINTS Provide opportunities for practical work to reinforce this learning. Illustrate line symmetry in a variety of contexts and check pupils understanding. It is important to demonstrate examples where the line of symmetry is not parallel to the edge of the page exercise. Star Challenges and illustrate the level of difficulty required at Level. KEY VOCABUL ARY mirror line line symmetry reflect reflection TO LEAR USE AND CROWN COPYRIGHT 00 50
5 PART SECTION Line symmetry and reflection Finding lines of symmetry Mirror Lines of symmetry are also called mirror lines. They are usually drawn like this Draw in ONE line of symmetry Draw in ALL lines of symmetry on each shape below: on the shapes below: Draw in any lines of symmetry in these road signs: A B C D E F G Regular polygons CROWN COPYRIGHT 00 A square has lines of symmetry Draw them. A regular hexagon has 6 lines of symmetry Draw them. A regular octagon has 8 lines of symmetry Draw them. 5
6 PART SECTION Line symmetry and reflection Mirror images Mirror This picture shows half a shape. Draw in the reflected shape, then check it with your mirror. mirror line Two mirror lines mirror line Reflect the shape in mirror line. Put your mirror on mirror line. Draw in their reflected shape. Make symmetric shapes Mirror Reflect each shading in the mirror line to make symmetric shapes: CROWN COPYRIGHT 00 5
7 PART SECTION Line symmetry and reflection Getting more difficult Mirror Reflect each shape in the mirror line(s): MAM S marks stars 6-0 marks star ( marks) ( marks) ( marks) ( marks) P ( marks) MALT ( marks) ( marks) ( marks) ( marks) A real challenge! Mirror CROWN COPYRIGHT 00 Reflect each shape BOTH WAYS in the mirror line to create symmetric patterns: correct shapes stars correct shapes stars correct shapes star 5
8 SECTIONS, AND : MEASURING ANGLES NAMING AND ESTIMATING ANGLES DRAWING ANGLES DIRECT TEACHING POINTS Consolidate measuring length (from Unit ) before going on to measure angles. Clarify the meaning of angle as a measure of turn and correct any misconceptions about its size being related to the length of the arms. Use an OHP to demonstrate the use of a protractor. Emphasise the correct use of the scale. Provide opportunities for pupils to use protractors with increasing accuracy. Measure this angle. I put the protractor like this. What did I do wrong? Teach the classification of angles and the use of correct vocabulary. Exercise provides practice. A right angle 90 An acute angle is less than 90 An obtuse angle is between 90 and 80 A reflex angle is bigger than 80 Model how to estimate the size of an angle using benchmarks such as 90, 80, and 5. Exercise and Star Challenge provide examples for discussion. Pupils need immediate feedback on their estimates in order to improve this important skill. Demonstrate the construction of triangles as in Section exercise. This is a sketch of a triangle. It is not drawn accurately. You are going to draw the triangle accurately A Start with the line BC, which is 0 cm long. Draw angle B, which is 0, then angle C, which is Extend the lines made by these angles so they B 0 cm cross. This is point A. Star Challenge 7 is quite demanding. You may need to consolidate basic ideas with some pupils. C CROWN COPYRIGHT 00 KEY TO VOCABUL ARY LEAR USE AND construct accurately straight line right angle degree acute angle obtuse angle reflex angle perpendicular parallel parallelogram angle full turn half turn quarter turn protractor 5
9 NNS Springboard 7 PART SPRINGBOARD 7 PART SECTION SECTION Measuring angles Measuring angles accurately (a) Measure each angle as accurately as you can. Write the answer next to the CROWN COPYRIGHT 00 (b) Now measure each angle as accurately as you can. Write the answer next to the. 55
10 PART SECTION Measuring angles Measuring angles Measure each of the angles. 0 marks stars 7-9 marks stars 5-6 marks star (a) ( mark) (b) ( mark) (c) ( mark) Measure all three marked angles: ( marks) Measure: ( marks) (a) the angle between the ladder and the ground. (b) the angle between the ladder and the wall. (c) the angle between the man s leg and the ladder. (d) the angle between the top of the man s arm and the ladder. CROWN COPYRIGHT 00 56
11 PART SECTION Naming and estimating angles Types of angle A right angle 90 An acute angle is less than 90 An obtuse angle is between 90 and 80 A reflex angle is bigger than 80 Is each marked angle acute, obtuse, reflex or a right-angle? This angle is This angle is 7 This angle is 0 This angle is 5 8 This angle is This angle is This angle is This angle is 6 9 CROWN COPYRIGHT 00 This angle is 0 This angle is This angle is 00 This angle is 57
12 PART SECTION Naming and estimating angles Estimating angles Estimate the size of each angle marked with a CROWN COPYRIGHT 00 58
13 PART SECTION Naming and estimating angles Estimation challenge Estimate the size of each angle: All correct star Mathematical word shapes 7-9 correct star Illustrate some mathematical words by writing them as the shape they describe. CROWN COPYRIGHT 00 Example A C U T E (acute) Try to do the same with these words: OBTUSE PARALLEL LINES HALF TURN FULL TURN PERPENDICULAR RIGHT ANGLE PARALLELOGRAMS TRIANGLE REFLEX 59
14 PART SECTION Drawing angles Constructing accurate triangles This is a sketch of a triangle. It is not drawn accurately. You are going to draw the triangle accurately. A Start with the line BC, which is 0 cm long. Draw angle B, which is 0, then angle C, which is 5. Extend the lines made by these angles so they cross. This is point A. B 0 0 cm 5 C B C Now measure the lengths of the lines AB and AC to the nearest 0. cm. AB cm AC cm Use the same method to draw triangle PQR accurately on the base line PQ below. Measure the other two sides of the triangle. R P 8 cm 5 Q CROWN COPYRIGHT 00 P Q PR cm QR cm 60
15 PART SECTION Drawing angles 6 Rotating patterns Both patterns accurately drawn star Rifat made this rotating pattern. She started with this flag. She drew a line at 5 to the stick of the flag to get this: 5 She then repeated the process. Each flag is at 5 to the previous flag. Copy this pattern in exactly the same way. Make sure your angles are exactly 5. Make another rotating pattern with the same flag. This time rotate the flag through CROWN COPYRIGHT 00 6
16 PART SECTION Drawing angles 7 More triangles Draw this diagram accurately. Measure the length of BC. A 5 cm 7 C 7.5 cm - marks stars 9- marks star B NOT DRAWN TO SCALE Draw this diagram accurately. Measure the length of PR. R. cm Q cm NOT DRAWN TO SCALE P Draw this diagram accurately. Measure the lengths of LM and MN. L NOT DRAWN TO SCALE 0 cm M N CROWN COPYRIGHT 00 marks for each drawing. mark for each measurement. 6
17 SECTION 5: CALCULATIONS INVOLVING ANGLES DIRECT TEACHING POINTS Take opportunities to practise relevant mental calculation skills, for example complements of 90 and 80. Make sure that pupils know and can use the fact that angles on a straight line add up to 80. Emphasise the difference between calculate and measure. KEY TO VOCABUL ARY LEAR USE AND parallel perpendicular straight line right angle CROWN COPYRIGHT 00 6
18 PART SECTION 5 Calculations involving angles Angles on a straight line Angles on a straight line add up to 80. b a a b 80 Example IDEA y 5 Find angle y 80-5 = 5, so y = 5û. Calculate each? angle. Do not use a protractor....? ?...? ?...? ?... CROWN COPYRIGHT 00 60? ? 6
19 PART SECTION 5 Calculations involving angles Working with right angles This symbol means a right angle. The angle is 90. Remember that angles on a straight line add up to 80û. Work out each of the angles: 5 a f g 56 a... f... g b 0 h h... 0 b... c 5 7 i j 75 i... j... CROWN COPYRIGHT 00 c e d 8 5 m k 5 d... e... k... m... 65
20 PART SECTION 5 Calculations involving angles 8 What s the angle? Calculate each angle: - correct stars 0- correct star a g h 0 a... g... h... 6 b 60 8 i j b... 0 d 7 i... j... c 0 m 5 c... d... f e n 70 k 5 CROWN COPYRIGHT 00 0 k... m... n... e... f... 66
21 PART ANSWERS Unit Answers Section Line symmetry and reflection Finding lines of symmetry Mirror images mirror line or axis of symmetry mirror line mirror line CROWN COPYRIGHT 00 Make symmetric shapes 67
22 PART ANSWERS Unit Answers Section Measuring angles Measuring angles accurately (a) (b) Section Naming and estimating angles Types of angle obtuse right 7 reflex 0 obtuse right 5 acute 8 right right acute 6 obtuse 9 acute reflex Estimating angles accept accept accept 0 0 accept accept accept 95 0 accept accept accept accept accept 0 60 accept 0 0 Section Drawing angles Constructing accurate triangles AB 5.9 or 6.0 cm PR 6. or 6.5 cm AC 6.6 or 6.7 cm QR 5.5 or 5.6 cm Section 5 Calculations involving angles Angles on a straight line CROWN COPYRIGHT Working with right angles a 90 d 90 e 0 7 i 05 j 90 b 60 5 f 90 g 8 k 55 m 5 68 c 75 6 h 0
23 S MAM MALT PART ANSWERS Unit Answers Star Challenge answers Getting more difficult marks stars 6-0 marks star MAM S P P MALT A real challenge! correct shapes stars correct shapes stars correct shapes star CROWN COPYRIGHT 00 Measuring angles 0 marks stars (a) 0 (b) 5 (c) marks stars 5-6 marks star (a) 65 (b) (c) (d) 5 Estimation challenge accept 0 70 accept 5-50 accept 5 5 accept accept 0 0 accept 0 0 accept 0 0 accept 0 0 All correct star 69
24 PART ANSWERS Unit Answers 5 6 Star Challenge answers Mathematical word shapes (Suggested shapes; others are possible) Rotating patterns continued O P E B R N F U S L T U S E U T L L M A R G O (obtuse) (full turn) (parallelograms) P A L R I A N L E L S E L P E N D I C U L A R R (perpendicular) E P (parallel lines) R I G H A R A L L T A N G L E (right angle) I 7-9 correct star F L E X E R (reflex) T R E A N G L (triangle) H N A R L F T U (half turn) Both patterns accurately drawn star Check all angles are 5 More triangles BC 7.7 cm. So, if BC cm, the diagram is likely to be fairly accurate. PR. cm. So, if PR.. cm, the diagram is likely to be fairly accurate. Check all angles are 60 - marks stars 9- marks star MN.5 cm and LM cm. So, if MN..6 cm and LM 0.9. cm, the diagram is likely to be fairly accurate. What s the angle? - correct stars a 05 5 g 60 h 0 0- correct star b 0 6 i 7 j 98 c 70 d 60 7 k 5 m 65 n 0 e 50 f 0 CROWN COPYRIGHT 00
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